RC Circuits Oscilloscope Challenge — PHY 162Lab
In this lab you will create simple RC circuits and measure their time constant
= RC by use of a harmonic signal generator, an oscilloscope and a PC. You will
collect (Voltage vs. Time) data on the oscilloscope screen and transfer it to the PC
using a memory module. You will then graph the data using Excel and fit it to an
exponential decay: V(t) = V0 exp(-t), where . When you make an Excel
graph with exponential fit for one of the (4) basic arrangements, you should print
the graph and include it in your lab report.
Exercises: The instructions in the standard lab manual will help you learn how to
use the oscilloscope. You are instructed to do two simple exercises: battery voltage
measurement and frequency measurement. You need not record the values of the
measurements, but be sure to show your instructor that the results are consistent
with expectations.
Main Procedure
Basic Arrangements: You will receive two resistors and two capacitors of
unknown values (R1, R2, C1, C2). Measure the time constants of all possible
simple combinations (; where ij = Ri*Cj) by making an exponential
fit to the data. First collect the V vs. t data and place it in an Excel file. Then
normalize the potential (V →V’ = V/V0) and rest the time (t→t’ = t-t0). Finally, use
Excel to find the best exponential fit: V’ = exp(-t’), with  = 1/.
Finding the basic R and C values: You may use the measured () values to find
suitable R and C values for the resistors and capacitors, but only up to a mutual
reciprocal factor. I.e., if (R1, R2, C1, C2) is a possible solution and  is a number,
then another possible solution is (R1, R2, C1/, C2/). However, if one of the
values is known (e.g., R1, measured with a multimeter), the other three values (R2,
C1, C2) can be calculated from the measured () values.
Error Estimate: You will find that there is more than one way to find suitable
values of (R2, C1, C2) using R1 and the () values. Use any method that seems
reasonable and fits the data, but also calculate an error estimate, to be used in
verifying your predictions for new arrangements:
% Error = 100%* |2*()/()|.
New Arrangements: You will then create circuits with different time constants
by combining the resistors and capacitors in new ways, including series and
parallel connections of the resistors, and series and parallel connections of the
capacitors. (There are twelve new possible combinations.) For each new circuit,
you will design it with a diagram, predict its time constant, construct the circuit
and verify the time constant experimentally. The value of % Error calculated above
gives an estimate of the accuracy you should expect.
The CHALLENGE: Predict and verify as many new time constants as possible.
You should be able to complete at least one prediction and verification…
Lab Report: Your will hand in your report at the end of the class period. It will
contain the following.
Basic arrangements (Table, 4 graphs)
1) Table: measured values of ( ), calculated % Error, determined values of (R1,
R2, C1, C2).
2) Graphs with exponential fits: one for each RC combination.
New arrangements (Table, diagrams and calculations)
3) For each new arrangement: Handwritten diagram and calculation of R and C.
4) Table: values of (R, C, predict, exp, %Diff, YES or NO), where R and C are
known or calculated, predict = RC, is the exponent fit to the data, exp= 1/ and
%Diff = 100%*|predict - exp |/ exp. YES or NO: Was the prediction correct?